This document provides summaries and examples of various mathematical topics including: - Arithmetic properties such as associative, commutative, and distributive properties - Exponent properties and properties of inequalities - Steps for solving quadratic equations - Algebra properties and calculus topics such as derivatives, limits, and integrals - Geometric shapes and solids and their volume formulas - Trigonometric functions, inverse trig functions, trig identities, and law of sines, cosines, and tangents.

1. ARITHMETIC PROPERTIES
ASSOCIATIVE
COMMUTATIVE
DISTRIBUTIVE
ARITHMETIC OPERATIONS EXAMPLES
EXPONENT PROPERTIES PROPERTIES OF INEQUALITIES
PROPERTIES OF COMPLEX NUMBERS
ABSOLUTE VALUE
LOGARITHM PROPERTIES
QUADRATIC EQUATION
For the equation
RADICAL PROPERTIES
COMMON FACTORING EXAMPLES
COMPLETING THE SQUARE
1. Divide by the coefficient a.
2. Move the constant to the other side.
3. Take half of the coefficient b/a, square
it and add it to both sides.
4. Factor the left side of the equation.
5. Use the square root property.
6. Solve for x.
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ALGEBRA PROPERTIES

2. DERIVATIVE DEFINITION
BASIC PROPERTIES
CHAIN RULE AND OTHER EXAMPLES
MEAN VALUE THEOREM
PRODUCT RULE
QUOTIENT RULE
POWER RULE
CHAIN RULE
COMMON DERIVATIVES
PROPERTIES OF LIMITS
LIMIT EVALUATIONS AT +-
LIMIT EVALUATION METHOD – FACTOR AND CANCEL
L’HOPITAL’S RULE
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CALCULUS DERIVATIVES AND LIMITS

3. `
where and
INTEGRATION BY SUBSTITUTION
COMMON INTEGRALS
or
INTEGRATION BY PARTS
INTEGRATION PROPERTIES
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Left-hand and right-hand rectangle approximations
Midpoint Rule
Trapezoid Rule
APPROXIMATING DEFINITE INTEGRALS
APPROXIMATION BY SIMPSON RULE FOR EVEN N
CALCULUS INTEGRALS
EXPRESSION EVALUATIONSUBSTITUTION IDENTITY USEDEXPRESSION
TRIGNOMETRIC SUBSTITUTION
DEFINITE INTEGRAL DEFINITION
where and
FUNDAMENTAL THEOREM OF CALCULUS
where f is continuous on [a,b] and

4. FRUSTUM OF A CONE
SQUARE RECTANGLE CIRCLE
TRIANGLE
CIRCULAR RING SPHERE
CUBE
RECTANGULAR BOX
CYLINDER
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CIRCULAR SECTOR
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TRAPEZOID
PYTHAGOREAN THEOREM
RIGHT CIRCULAR CONE
GEOMETRY SHAPES AND SOLIDS
PARALLELOGRAM

5. RIGHT TRIANGLE DEFINITION
UNIT CIRCLE DEFINITION TRIG FUNCTIONS DOMAIN
TRIG FUNCTIONS RANGE
TRIG FUNCTIONS PERIOD
INVERSE TRIG FUNCTION NOTATION
INVERSE TRIG FUNCTION RANGE
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TRIGONOMETRY DEFINITION
INVERSE TRIG DOMAIN

6. TANGENT IDENTITIES RECIPROCAL IDENTITIES PYTHAGOREAN IDENTITIES
IDENTITIES
PERIODIC IDENTITIES
IDENTITIES
EVEN/ODD IDENTITIES
IDENTITIES
DOUBLE ANGLE IDENTITIES HALF ANGLE IDENTITIES
ITIES
TRIGONOMETRY
SUM/DIFFERENCES IDENTITIES
PRODUCT TO SUM IDENTITIES SUM TO PRODUCT IDENTITIES
COFUNCTION IDENTITIES
RIGHT TRIANGLE DEFINIT
TRIGONO
LAW OF SINES
LAW OF COSINES
LAW OF TANGENTS
MOLLWEIDE’S FORMULA
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LAWS AND IDENTITIES